Problem: Simplify the following expression: ${5(-5r+5)+7(-2+8r)}$
Distribute the ${5}$ into the first set of parentheses: $ {5(}\gray{-5r+5}{)} + 7(-2+8r) $ $ {-25r+25} + 7(-2+8r) $ Distribute the ${7}$ into the parentheses: $ -25r+25 + {7(}\gray{-2+8r}{)} $ $ -25r+25 {-14+56r} $ Rewrite the expression to group the ${r}$ terms and numeric terms: $ {-25r + 56r} + {25 - 14}$ Combine the ${r}$ terms: $ {31r} + {25 - 14}$ Combine the numeric terms: $ {31r} + {11}$ The simplified expression is $31r+11$